So far, we have evaluated the log ratio of path probabilities
following the standard approach. As an alternative, we now employ a
fractional differential approach
[1]}, [2]}, [3]}. To start with,
we integrate Eq. (REF ) over time, yielding
\({x}(t)-x_0= \mu \bar{F}(x(t), \lambda (t))+ \xi ^H_{fBm}(t) ,\) 
